import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
import numpy as np
import sklearn as sk
from sklearn.linear_model import LinearRegression
import statsmodels.api as sm
import statsmodels.formula.api as smf
from bokeh.plotting import figure, output_file, show
from bokeh.palettes import magma
from bokeh.models import ColumnDataSource
from plotnine import ggplot, aes, geom_point, theme_minimal, labs, theme, element_blank
from sklearn.experimental import enable_iterative_imputer
from sklearn.impute import IterativeImputer
import statsmodels.stats.diagnostic as ssd
import  statsmodels.stats.outliers_influence as oi
import statsmodels.stats.anova as av
import statsmodels.stats.oneway as ow
from statsmodels.tsa.stattools import adfuller

nhanes =pd.read_csv("clenning.ipynb (cnhanes).csv")

n_nhanes = nhanes.select_dtypes(include=['float'])

n_nhanes.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 10349 entries, 0 to 10348
Data columns (total 21 columns):
 #   Column    Non-Null Count  Dtype  
---  ------    --------------  -----  
 0   sampl     10349 non-null  float64
 1   strata    10349 non-null  float64
 2   location  10349 non-null  float64
 3   height    10349 non-null  float64
 4   weight    10349 non-null  float64
 5   tcresult  10349 non-null  float64
 6   hdresult  10349 non-null  float64
 7   hgb       10349 non-null  float64
 8   hct       10349 non-null  float64
 9   tibc      10349 non-null  float64
 10  iron      10349 non-null  float64
 11  finalwgt  10349 non-null  float64
 12  leadwt    10349 non-null  float64
 13  corpuscl  10349 non-null  float64
 14  trnsfern  10349 non-null  float64
 15  albumin   10349 non-null  float64
 16  vitaminc  10349 non-null  float64
 17  zinc      10349 non-null  float64
 18  copper    10349 non-null  float64
 19  porphyrn  10349 non-null  float64
 20  bmi       10349 non-null  float64
dtypes: float64(21)
memory usage: 1.7 MB

percentiles = n_nhanes.quantile([0.1, 0.9])

# Apply filtering for each column
for column in n_nhanes.columns:
    low = percentiles.loc[0.1]
    high = percentiles.loc[0.9]
    abdo = n_nhanes[(n_nhanes >= low) &(n_nhanes<=high)]

print(abdo.info())

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 10349 entries, 0 to 10348
Data columns (total 21 columns):
 #   Column    Non-Null Count  Dtype  
---  ------    --------------  -----  
 0   sampl     8279 non-null   float64
 1   strata    8679 non-null   float64
 2   location  8341 non-null   float64
 3   height    8284 non-null   float64
 4   weight    8295 non-null   float64
 5   tcresult  8303 non-null   float64
 6   hdresult  8368 non-null   float64
 7   hgb       8414 non-null   float64
 8   hct       8371 non-null   float64
 9   tibc      8314 non-null   float64
 10  iron      8359 non-null   float64
 11  finalwgt  8282 non-null   float64
 12  leadwt    9314 non-null   float64
 13  corpuscl  8320 non-null   float64
 14  trnsfern  8307 non-null   float64
 15  albumin   8700 non-null   float64
 16  vitaminc  9146 non-null   float64
 17  zinc      8446 non-null   float64
 18  copper    8366 non-null   float64
 19  porphyrn  8360 non-null   float64
 20  bmi       8279 non-null   float64
dtypes: float64(21)
memory usage: 1.7 MB
None

imputer = IterativeImputer()
fit_imput = imputer.fit_transform(abdo)
cabdo = pd.DataFrame(fit_imput, columns = abdo.columns)

cabdo.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 10349 entries, 0 to 10348
Data columns (total 21 columns):
 #   Column    Non-Null Count  Dtype  
---  ------    --------------  -----  
 0   sampl     10349 non-null  float64
 1   strata    10349 non-null  float64
 2   location  10349 non-null  float64
 3   height    10349 non-null  float64
 4   weight    10349 non-null  float64
 5   tcresult  10349 non-null  float64
 6   hdresult  10349 non-null  float64
 7   hgb       10349 non-null  float64
 8   hct       10349 non-null  float64
 9   tibc      10349 non-null  float64
 10  iron      10349 non-null  float64
 11  finalwgt  10349 non-null  float64
 12  leadwt    10349 non-null  float64
 13  corpuscl  10349 non-null  float64
 14  trnsfern  10349 non-null  float64
 15  albumin   10349 non-null  float64
 16  vitaminc  10349 non-null  float64
 17  zinc      10349 non-null  float64
 18  copper    10349 non-null  float64
 19  porphyrn  10349 non-null  float64
 20  bmi       10349 non-null  float64
dtypes: float64(21)
memory usage: 1.7 MB

i_nhanes =nhanes.select_dtypes(include=['int'])
o_nhanes = nhanes.select_dtypes(include=['object'])

nhanes = pd.concat([cabdo,i_nhanes,o_nhanes],axis=1)

nhanes.hist(figsize=(20,20))

array([[<Axes: title={'center': 'sampl'}>,
        <Axes: title={'center': 'strata'}>,
        <Axes: title={'center': 'location'}>,
        <Axes: title={'center': 'height'}>,
        <Axes: title={'center': 'weight'}>,
        <Axes: title={'center': 'tcresult'}>],
       [<Axes: title={'center': 'hdresult'}>,
        <Axes: title={'center': 'hgb'}>, <Axes: title={'center': 'hct'}>,
        <Axes: title={'center': 'tibc'}>,
        <Axes: title={'center': 'iron'}>,
        <Axes: title={'center': 'finalwgt'}>],
       [<Axes: title={'center': 'leadwt'}>,
        <Axes: title={'center': 'corpuscl'}>,
        <Axes: title={'center': 'trnsfern'}>,
        <Axes: title={'center': 'albumin'}>,
        <Axes: title={'center': 'vitaminc'}>,
        <Axes: title={'center': 'zinc'}>],
       [<Axes: title={'center': 'copper'}>,
        <Axes: title={'center': 'porphyrn'}>,
        <Axes: title={'center': 'bmi'}>,
        <Axes: title={'center': 'houssiz'}>,
        <Axes: title={'center': 'age'}>,
        <Axes: title={'center': 'bpsystol'}>],
       [<Axes: title={'center': 'bpdiast'}>,
        <Axes: title={'center': 'hsizgp'}>,
        <Axes: title={'center': 'highbp'}>,
        <Axes: title={'center': 'smsa_all'}>,
        <Axes: title={'center': 'region_all'}>,
        <Axes: title={'center': 'psu'}>],
       [<Axes: title={'center': 'sex'}>,
        <Axes: title={'center': 'race'}>,
        <Axes: title={'center': 'heartatk'}>,
        <Axes: title={'center': 'diabetes'}>,
        <Axes: title={'center': 'rural'}>, <Axes: >]], dtype=object)

nhanes.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 10349 entries, 0 to 10348
Data columns (total 37 columns):
 #   Column      Non-Null Count  Dtype  
---  ------      --------------  -----  
 0   sampl       10349 non-null  float64
 1   strata      10349 non-null  float64
 2   location    10349 non-null  float64
 3   height      10349 non-null  float64
 4   weight      10349 non-null  float64
 5   tcresult    10349 non-null  float64
 6   hdresult    10349 non-null  float64
 7   hgb         10349 non-null  float64
 8   hct         10349 non-null  float64
 9   tibc        10349 non-null  float64
 10  iron        10349 non-null  float64
 11  finalwgt    10349 non-null  float64
 12  leadwt      10349 non-null  float64
 13  corpuscl    10349 non-null  float64
 14  trnsfern    10349 non-null  float64
 15  albumin     10349 non-null  float64
 16  vitaminc    10349 non-null  float64
 17  zinc        10349 non-null  float64
 18  copper      10349 non-null  float64
 19  porphyrn    10349 non-null  float64
 20  bmi         10349 non-null  float64
 21  houssiz     10349 non-null  int64  
 22  age         10349 non-null  int64  
 23  bpsystol    10349 non-null  int64  
 24  bpdiast     10349 non-null  int64  
 25  hsizgp      10349 non-null  int64  
 26  highbp      10349 non-null  int64  
 27  smsa_all    10349 non-null  int64  
 28  region_all  10349 non-null  int64  
 29  psu         10349 non-null  int64  
 30  sex         10349 non-null  int64  
 31  race        10349 non-null  int64  
 32  heartatk    10349 non-null  int64  
 33  diabetes    10349 non-null  int64  
 34  rural       10349 non-null  int64  
 35  hlthstat    10349 non-null  object 
 36  sizplace    10349 non-null  object 
dtypes: float64(21), int64(14), object(2)
memory usage: 2.9+ MB

nhanes.head()

nhanes.describe()

num_nhanes = nhanes.select_dtypes(include=['number'])

int_nhanes = nhanes.select_dtypes(include=['int'])

obj_nhanes = nhanes.select_dtypes(include=['object'])

sns.set_palette("Set3")

# Assuming 'int_nhanes' is a list of column names and 'num_nhanes' is a DataFrame
for column in int_nhanes:
    plt.figure(figsize=(15, 8))
    
    # Skip certain columns
    if column in ['age', 'houssize', 'bpsystol']:
        continue

    # Plot the bar chart
    num_nhanes[column].value_counts().plot(kind='bar', color=sns.color_palette("Set3"), edgecolor='black')

    # Add labels and title
    plt.title(f'Distribution of {column}')
    plt.xlabel(f'{column}')
    plt.ylabel('Count')

    # Display the chart
    plt.show()

<Figure size 1500x800 with 0 Axes>

<Figure size 1500x800 with 0 Axes>

# Set a color palette for better visualization
sns.set_palette("pastel")

# Assuming 'obj_nhanes' is a DataFrame
for column in obj_nhanes:
    plt.figure(figsize=(12, 8))
    
    # Plot the bar chart
    obj_nhanes[column].value_counts().plot(kind='bar', color=sns.color_palette("pastel"), edgecolor='black')

    # Add labels and title
    plt.title(f'Distribution of {column}', fontsize=16)
    plt.xlabel(f'{column}', fontsize=14)
    plt.ylabel('Count', fontsize=14)

    # Add data labels on top of the bars
    for i, value in enumerate(obj_nhanes[column].value_counts()):
        plt.text(i, value + 0.1, str(value), ha='center', va='bottom', fontsize=12)

    # Display the chart
    plt.show()

# Set a custom color palette
custom_palette = sns.color_palette("coolwarm", as_cmap=True)

# Set up the matplotlib figure
plt.figure(figsize=(20, 15))

# Create a heatmap with correlation values annotated
heatmap = sns.heatmap(
    num_nhanes.corr(),
    annot=True,
    cmap=custom_palette,
    fmt=".2f",
    linewidths=0.5,
    annot_kws={"size": 12},
)

# Customize the aesthetics
heatmap.set_title("Correlation Heatmap", fontsize=18, fontweight='bold')

# Rotate the y-axis ticks for better readability
plt.yticks(rotation=0)

# Add color bar with labeled values
cbar = heatmap.collections[0].colorbar
cbar.ax.tick_params(labelsize=12)
cbar.set_label('Correlation Coefficient', fontsize=14)

# Add a shadow to the annotation for better contrast
for _, spine in heatmap.spines.items():
    spine.set_visible(True)
    spine.set_linewidth(1.5)
    spine.set_edgecolor("darkgray")

# Adjust layout for better spacing
plt.tight_layout()

# Show the heatmap
plt.show()

import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns

# Assuming num_nhanes is your DataFrame
# Make sure to replace it with your actual DataFrame

# Your plotting code with additional styling
fig, axes = plt.subplots(nrows=len(num_nhanes.columns), figsize=(15, 70), sharex=False)

# Use a professional Seaborn style
sns.set(style="whitegrid")

# Define a color palette for the box plots
custom_palette = sns.color_palette("husl")

for i, column in enumerate(num_nhanes.columns):
    sns.boxplot(x=num_nhanes[column], ax=axes[i], color=custom_palette[i % len(custom_palette)])
    axes[i].set_title(column, fontsize=16)
    axes[i].tick_params(labelsize=12)

# Adjust layout for better spacing
plt.tight_layout()

plt.suptitle("Box Plots of Numeric Variables", y=0.92, fontsize=20)
plt.show()

# Set Seaborn theme and color palette
sns.set_theme()
#sns.set_palette("husl")  # You can choose a different palette, for example, "coolwarm"
custom_palette = sns.color_palette("husl", n_colors=len(nhanes.columns))
# Create a scatter matrix
scatter_matrix = pd.plotting.scatter_matrix(nhanes, figsize=(20, 20), diagonal="hist", alpha=0.7)

# Customize scatter matrix with Seaborn style
for ax in scatter_matrix.flatten():
    ax.xaxis.label.set_rotation(45)
    ax.yaxis.label.set_rotation(0)
    ax.yaxis.label.set_ha('right')

# Adjust layout
plt.tight_layout()

# Show the plot
plt.show()

# Set a custom color palette
custom_palette = sns.color_palette("husl", n_colors=len(nhanes.columns))

# Set up subplots
fig, axes = plt.subplots(nrows=len(nhanes.columns) // 2 + 1, ncols=2, figsize=(30, 70), sharex=False)

# Flatten the axes array to iterate over them
axes = axes.flatten()

# Iterate through each column and create a histogram
for i, column in enumerate(nhanes.columns):
    sns.histplot(nhanes[column], bins=20, ax=axes[i], color=custom_palette[i], kde=True)
    axes[i].set_title(f'Histogram for {column}', fontsize=16)
    axes[i].set_xlabel(column, fontsize=14)
    axes[i].set_ylabel('Frequency', fontsize=14)
    axes[i].grid(axis='y', linestyle='--', alpha=0.7)

# Remove empty subplots if there are an odd number of columns
if len(nhanes.columns) % 2 != 0:
    fig.delaxes(axes[-1])

# Adjust layout for better spacing
plt.tight_layout()

# Show the histograms
plt.show()

bmi_model = smf.ols('bmi~height+weight',data=nhanes).fit()

print(bmi_model.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:                    bmi   R-squared:                       0.997
Model:                            OLS   Adj. R-squared:                  0.997
Method:                 Least Squares   F-statistic:                 1.990e+06
Date:                Sun, 21 Jan 2024   Prob (F-statistic):               0.00
Time:                        23:23:29   Log-Likelihood:                 4277.8
No. Observations:               10349   AIC:                            -8550.
Df Residuals:                   10346   BIC:                            -8528.
Df Model:                           2                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
Intercept     50.4737      0.032   1556.250      0.000      50.410      50.537
height        -0.3013      0.000  -1357.078      0.000      -0.302      -0.301
weight         0.3561      0.000   1957.806      0.000       0.356       0.357
==============================================================================
Omnibus:                      776.160   Durbin-Watson:                   1.997
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             3369.235
Skew:                           0.247   Prob(JB):                         0.00
Kurtosis:                       5.751   Cond. No.                     3.76e+03
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 3.76e+03. This might indicate that there are
strong multicollinearity or other numerical problems.

residuals = bmi_model.resid
fitted = bmi_model.fittedvalues
# Set seaborn style
sns.set(style="whitegrid")

# Create subplots
fig, axs = plt.subplots(2, 2, figsize=(20, 15))

# QQ Plot of Residuals
sm.qqplot(residuals, line='s', ax=axs[0, 0])
axs[0, 0].set_title('QQ Plot of Residuals')
axs[0, 0].grid(True, linestyle='--', alpha=0.5)

# Residuals vs Fitted Values
axs[0, 1].scatter(fitted, residuals, alpha=0.7, color='green')
axs[0, 1].axhline(y=0, color='red', linestyle='--')
axs[0, 1].set_xlabel('Fitted Values')
axs[0, 1].set_ylabel('Residuals')
axs[0, 1].set_title('Residuals vs Fitted Values')
axs[0, 1].grid(True, linestyle='--', alpha=0.5)

# Histogram of Residuals
axs[1, 0].hist(residuals, bins=15, edgecolor='black', color='blue', alpha=0.7)
axs[1, 0].set_title('Histogram of Residuals')
axs[1, 0].set_xlabel('Residuals')
axs[1, 0].set_ylabel('Frequency')
axs[1, 0].grid(True, linestyle='--', alpha=0.5)

# Boxplot of Residuals
sns.boxplot(x=residuals, ax=axs[1, 1], color='orange')
axs[1, 1].set_title('Boxplot of Residuals')
axs[1, 1].set_xlabel('Residuals')
axs[1, 1].grid(True, linestyle='--', alpha=0.5)

# Adjust layout
plt.tight_layout()
plt.show()

influence = oi.OLSInfluence(bmi_model).summary_frame()
influence

# Assuming 'bmi_model' is your regression model and 'influence' is the influence object

k = len(bmi_model.params) - 1  # subtracting 1 for the intercept
n = len(num_nhanes)

# Thresholds
leverage_threshold = 3 * (k + 1) / n
cooks_d_threshold1 = 0.5  # Somewhat influential
cooks_d_threshold2 = 1    # Excessively influential

# Create subplots for each criterion
fig, axs = plt.subplots(1, 3, figsize=(18, 6))

# Studentized Residuals Plot
axs[0].scatter(range(n), influence["student_resid"], color='blue', alpha=0.7, label='Residuals')
axs[0].axhline(y=3, color='red', linestyle='--', label='Threshold')
axs[0].axhline(y=-3, color='red', linestyle='--')
axs[0].set_xlabel('Observation')
axs[0].set_ylabel('Studentized Residuals')
axs[0].set_title('Studentized Residuals with ±3 Threshold')
axs[0].legend(loc='upper right')
axs[0].grid(True, linestyle='--', alpha=0.5)

# Leverage Plot
axs[1].scatter(range(n), influence["hat_diag"], color='green', alpha=0.7, label='Leverage')
axs[1].axhline(y=leverage_threshold, color='red', linestyle='--', label='Threshold')
axs[1].set_xlabel('Observation')
axs[1].set_ylabel('Leverage')
axs[1].set_title('Leverage Values with Threshold')
axs[1].legend(loc='upper right')
axs[1].grid(True, linestyle='--', alpha=0.5)

# Cook's Distance Plot
axs[2].scatter(range(n), influence["cooks_d"], marker='o', color='red', label="Cook's Distance")
axs[2].axhline(y=cooks_d_threshold1, color='orange', linestyle='--', label='Threshold 1')
axs[2].axhline(y=cooks_d_threshold2, color='red', linestyle='--', label='Threshold 2')
axs[2].set_xlabel('Observation')
axs[2].set_ylabel("Cook's Distance")
axs[2].set_title("Cook's Distance with Thresholds")
axs[2].legend(loc='upper right')
axs[2].grid(True, linestyle='--', alpha=0.5)

plt.tight_layout()
plt.show()

bmi_hetro = ssd.het_breuschpagan(bmi_model.resid,bmi_model.model.exog)
bmi_hetro_test_statistic, bmi_hetro_p_value = bmi_hetro[:2]
bmi_hetro_test_statistic, bmi_hetro_p_value

(21.08146087890606, 2.643741174396657e-05)

bmi_model_t = smf.ols('np.log(bmi)~np.log(height)+np.log(weight)',data=nhanes).fit()
bmi_model_t.summary()

residuals = bmi_model_t.resid
fitted = bmi_model_t.fittedvalues
# Set seaborn style
sns.set(style="whitegrid")

# Create subplots
fig, axs = plt.subplots(2, 2, figsize=(20, 15))

# QQ Plot of Residuals
sm.qqplot(residuals, line='s', ax=axs[0, 0])
axs[0, 0].set_title('QQ Plot of Residuals')
axs[0, 0].grid(True, linestyle='--', alpha=0.5)

# Residuals vs Fitted Values
axs[0, 1].scatter(fitted, residuals, alpha=0.7, color='green')
axs[0, 1].axhline(y=0, color='red', linestyle='--')
axs[0, 1].set_xlabel('Fitted Values')
axs[0, 1].set_ylabel('Residuals')
axs[0, 1].set_title('Residuals vs Fitted Values')
axs[0, 1].grid(True, linestyle='--', alpha=0.5)

# Histogram of Residuals
axs[1, 0].hist(residuals, bins=15, edgecolor='black', color='blue', alpha=0.7)
axs[1, 0].set_title('Histogram of Residuals')
axs[1, 0].set_xlabel('Residuals')
axs[1, 0].set_ylabel('Frequency')
axs[1, 0].grid(True, linestyle='--', alpha=0.5)

# Boxplot of Residuals
sns.boxplot(x=residuals, ax=axs[1, 1], color='orange')
axs[1, 1].set_title('Boxplot of Residuals')
axs[1, 1].set_xlabel('Residuals')
axs[1, 1].grid(True, linestyle='--', alpha=0.5)

# Adjust layout
plt.tight_layout()
plt.show()

influence_1 = oi.OLSInfluence(bmi_model_t).summary_frame()
influence_1

k = len(bmi_model_t.params) - 1  # subtracting 1 for the intercept
n = len(num_nhanes)

# Thresholds
leverage_threshold = 3 * (k + 1) / n
cooks_d_threshold1 = 0.5  # Somewhat influential
cooks_d_threshold2 = 1    # Excessively influential

# Create subplots for each criterion
fig, axs = plt.subplots(1, 3, figsize=(18, 6))

# Studentized Residuals Plot
axs[0].scatter(range(n), influence_1["student_resid"])
axs[0].axhline(y=3, color='red', linestyle='--')
axs[0].axhline(y=-3, color='red', linestyle='--')
axs[0].set_xlabel('Observation')
axs[0].set_ylabel('Studentized Residuals')
axs[0].set_title('Studentized Residuals with ±3 Threshold')

# Leverage Plot
axs[1].scatter(range(n), influence_1["hat_diag"])
axs[1].axhline(y=leverage_threshold, color='red', linestyle='--')
axs[1].set_xlabel('Observation')
axs[1].set_ylabel('Leverage')
axs[1].set_title('Leverage Values with Threshold')

# Cook's Distance Plot
axs[2].stem(influence_1["cooks_d"])
axs[2].axhline(y=cooks_d_threshold1, color='orange', linestyle='--')
axs[2].axhline(y=cooks_d_threshold2, color='red', linestyle='--')
axs[2].set_xlabel('Observation')
axs[2].set_ylabel("Cook's Distance")
axs[2].set_title("Cook's Distance with Thresholds")

plt.tight_layout()
plt.show()

bmi_hetro_t = ssd.het_breuschpagan(bmi_model_t.resid,bmi_model_t.model.exog)

bmi_hetro_t_test_statistic, bmi_hetro_p_value = bmi_hetro_t[:2]
bmi_hetro_t_test_statistic, bmi_hetro_p_value

(127.63116653264774, 1.9286096168244454e-28)

waight =1/(bmi_model.resid**2)

bmi_model_weight = smf.wls('bmi~height+weight',data=nhanes,weights=waight).fit()

bmi_model_weight.summary()

residuals = bmi_model_weight.resid
fitted = bmi_model_weight.fittedvalues

fig, axs = plt.subplots(2, 2, figsize=(20, 15))

sm.qqplot(residuals, line='s', ax=axs[0,0])
axs[0,0].set_title('QQ Plot of Residuals')

axs[0,1].scatter(fitted, residuals)
axs[0,1].axhline(y=0, color='red', linestyle='--')
axs[0,1].set_xlabel('Fitted Values')
axs[0,1].set_ylabel('Residuals')
axs[0,1].set_title('Residuals vs Fitted Values')

axs[1,0].hist(residuals, bins=15, edgecolor='black')
axs[1,0].set_title('Histogram of Residuals')

sns.boxplot(residuals, ax= axs[1,1])
axs[1,1].set_title('Boxplot of Residuals')

plt.tight_layout()
plt.show()

influence_2 = oi.OLSInfluence(bmi_model_weight).summary_frame()
influence_2

k = len(bmi_model_weight.params) - 1  # subtracting 1 for the intercept
n = len(num_nhanes)

# Thresholds
leverage_threshold = 3 * (k + 1) / n
cooks_d_threshold1 = 0.5  # Somewhat influential
cooks_d_threshold2 = 1    # Excessively influential

# Create subplots for each criterion
fig, axs = plt.subplots(1, 3, figsize=(18, 6))

# Studentized Residuals Plot
axs[0].scatter(range(n), influence_2["student_resid"])
axs[0].axhline(y=3, color='red', linestyle='--')
axs[0].axhline(y=-3, color='red', linestyle='--')
axs[0].set_xlabel('Observation')
axs[0].set_ylabel('Studentized Residuals')
axs[0].set_title('Studentized Residuals with ±3 Threshold')

# Leverage Plot
axs[1].scatter(range(n), influence_2["hat_diag"])
axs[1].axhline(y=leverage_threshold, color='red', linestyle='--')
axs[1].set_xlabel('Observation')
axs[1].set_ylabel('Leverage')
axs[1].set_title('Leverage Values with Threshold')

# Cook's Distance Plot
axs[2].stem(influence_2["cooks_d"])
axs[2].axhline(y=cooks_d_threshold1, color='orange', linestyle='--')
axs[2].axhline(y=cooks_d_threshold2, color='red', linestyle='--')
axs[2].set_xlabel('Observation')
axs[2].set_ylabel("Cook's Distance")
axs[2].set_title("Cook's Distance with Thresholds")

plt.tight_layout()
plt.show()

bmi_hetro_weight = ssd.het_breuschpagan(bmi_model_weight.resid,bmi_model_weight.model.exog)
bmi_hetro_weight_test_statistic, bmi_hetro_weight_p_value = bmi_hetro_weight[:2]
bmi_hetro_weight_test_statistic, bmi_hetro_weight_p_value

(21.09803276419513, 2.621925791976834e-05)

bmi_model_weight_t = smf.wls('np.log(bmi)~np.log(height)+np.log(weight)',data=nhanes,weights=waight).fit()

bmi_model_weight_t.summary()

residuals = bmi_model_weight_t.resid
fitted = bmi_model_weight_t.fittedvalues

fig, axs = plt.subplots(2, 2, figsize=(20, 15))

sm.qqplot(residuals, line='s', ax=axs[0,0])
axs[0,0].set_title('QQ Plot of Residuals')

axs[0,1].scatter(fitted, residuals)
axs[0,1].axhline(y=0, color='red', linestyle='--')
axs[0,1].set_xlabel('Fitted Values')
axs[0,1].set_ylabel('Residuals')
axs[0,1].set_title('Residuals vs Fitted Values')

axs[1,0].hist(residuals, bins=15, edgecolor='black')
axs[1,0].set_title('Histogram of Residuals')

sns.boxplot(residuals, ax= axs[1,1])
axs[1,1].set_title('Boxplot of Residuals')

plt.tight_layout()
plt.show()

influence_3 = oi.OLSInfluence(bmi_model_weight_t).summary_frame()
influence_3

k = len(bmi_model_weight_t.params) - 1  # subtracting 1 for the intercept
n = len(num_nhanes)

# Thresholds
leverage_threshold = 3 * (k + 1) / n
cooks_d_threshold1 = 0.5  # Somewhat influential
cooks_d_threshold2 = 1    # Excessively influential

# Create subplots for each criterion
fig, axs = plt.subplots(1, 3, figsize=(18, 6))

# Studentized Residuals Plot
axs[0].scatter(range(n), influence_3["student_resid"])
axs[0].axhline(y=3, color='red', linestyle='--')
axs[0].axhline(y=-3, color='red', linestyle='--')
axs[0].set_xlabel('Observation')
axs[0].set_ylabel('Studentized Residuals')
axs[0].set_title('Studentized Residuals with ±3 Threshold')

# Leverage Plot
axs[1].scatter(range(n), influence_3["hat_diag"])
axs[1].axhline(y=leverage_threshold, color='red', linestyle='--')
axs[1].set_xlabel('Observation')
axs[1].set_ylabel('Leverage')
axs[1].set_title('Leverage Values with Threshold')

# Cook's Distance Plot
axs[2].stem(influence_3["cooks_d"])
axs[2].axhline(y=cooks_d_threshold1, color='orange', linestyle='--')
axs[2].axhline(y=cooks_d_threshold2, color='red', linestyle='--')
axs[2].set_xlabel('Observation')
axs[2].set_ylabel("Cook's Distance")
axs[2].set_title("Cook's Distance with Thresholds")

plt.tight_layout()
plt.show()

bmi_hetro_weight_t = ssd.het_breuschpagan(bmi_model_weight_t.resid,bmi_model_weight_t.model.exog)
bmi_hetro_weight_t_test_statistic, bmi_hetro_weight_t_p_value = bmi_hetro_weight_t[:2]
bmi_hetro_weight_t_test_statistic, bmi_hetro_weight_t_p_value

(712.5676722616203, 1.8530877156168763e-155)

#heart_model = smf.ols('(highbp)~bpdiast+bpsystol',data=nhanes).fit()
highbp_model = smf.logit('(highbp)~bpdiast+bpsystol',data=nhanes).fit()

Optimization terminated successfully.
         Current function value: 0.165689
         Iterations 10

print(highbp_model.summary())

                           Logit Regression Results                           
==============================================================================
Dep. Variable:                 highbp   No. Observations:                10349
Model:                          Logit   Df Residuals:                    10346
Method:                           MLE   Df Model:                            2
Date:                Sun, 21 Jan 2024   Pseudo R-squ.:                  0.7568
Time:                        23:25:34   Log-Likelihood:                -1714.7
converged:                       True   LL-Null:                       -7049.7
Covariance Type:            nonrobust   LLR p-value:                     0.000
==============================================================================
                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
Intercept    -49.6261      1.249    -39.741      0.000     -52.074     -47.179
bpdiast        0.2504      0.008     32.661      0.000       0.235       0.265
bpsystol       0.2176      0.006     36.483      0.000       0.206       0.229
==============================================================================

Possibly complete quasi-separation: A fraction 0.22 of observations can be
perfectly predicted. This might indicate that there is complete
quasi-separation. In this case some parameters will not be identified.

bpsystol_model = smf.ols('(bpsystol)~age+vitaminc+zinc',data=nhanes).fit()

bpsystol_model.summary()

residuals = bpsystol_model.resid
fitted = bpsystol_model.fittedvalues

fig, axs = plt.subplots(2, 2, figsize=(20, 15))

sm.qqplot(residuals, line='s', ax=axs[0,0])
axs[0,0].set_title('QQ Plot of Residuals')

axs[0,1].scatter(fitted, residuals)
axs[0,1].axhline(y=0, color='red', linestyle='--')
axs[0,1].set_xlabel('Fitted Values')
axs[0,1].set_ylabel('Residuals')
axs[0,1].set_title('Residuals vs Fitted Values')

axs[1,0].hist(residuals, bins=15, edgecolor='black')
axs[1,0].set_title('Histogram of Residuals')

sns.boxplot(residuals, ax= axs[1,1])
axs[1,1].set_title('Boxplot of Residuals')

plt.tight_layout()
plt.show()

influence_4 = oi.OLSInfluence(bpsystol_model).summary_frame()
influence_4

k = len(bpsystol_model.params) - 1  # subtracting 1 for the intercept
n = len(num_nhanes)

# Thresholds
leverage_threshold = 3 * (k + 1) / n
cooks_d_threshold1 = 0.5  # Somewhat influential
cooks_d_threshold2 = 1    # Excessively influential

# Create subplots for each criterion
fig, axs = plt.subplots(1, 3, figsize=(18, 6))

# Studentized Residuals Plot
axs[0].scatter(range(n), influence_4["student_resid"])
axs[0].axhline(y=3, color='red', linestyle='--')
axs[0].axhline(y=-3, color='red', linestyle='--')
axs[0].set_xlabel('Observation')
axs[0].set_ylabel('Studentized Residuals')
axs[0].set_title('Studentized Residuals with ±3 Threshold')

# Leverage Plot
axs[1].scatter(range(n), influence_4["hat_diag"])
axs[1].axhline(y=leverage_threshold, color='red', linestyle='--')
axs[1].set_xlabel('Observation')
axs[1].set_ylabel('Leverage')
axs[1].set_title('Leverage Values with Threshold')

# Cook's Distance Plot
axs[2].stem(influence_4["cooks_d"])
axs[2].axhline(y=cooks_d_threshold1, color='orange', linestyle='--')
axs[2].axhline(y=cooks_d_threshold2, color='red', linestyle='--')
axs[2].set_xlabel('Observation')
axs[2].set_ylabel("Cook's Distance")
axs[2].set_title("Cook's Distance with Thresholds")

plt.tight_layout()
plt.show()

bpsystol_hetro = ssd.het_breuschpagan(bpsystol_model.resid,bpsystol_model.model.exog)
bpsystol_hetro_test_statistic, bpsystol_hetro_p_value = bpsystol_hetro[:2]
bpsystol_hetro_test_statistic, bpsystol_hetro_p_value

(334.4605429370067, 3.453195126162539e-72)

waight =1/(bpsystol_model.resid**2)

w_bpsystol_model=smf.wls('np.log(bpsystol)~np.log(age)+np.log(vitaminc)+np.log(zinc)',data=nhanes,weights=waight).fit()

print(w_bpsystol_model.summary())

                            WLS Regression Results                            
==============================================================================
Dep. Variable:       np.log(bpsystol)   R-squared:                       0.999
Model:                            WLS   Adj. R-squared:                  0.999
Method:                 Least Squares   F-statistic:                 4.882e+06
Date:                Sun, 21 Jan 2024   Prob (F-statistic):               0.00
Time:                        23:26:09   Log-Likelihood:                -5481.3
No. Observations:               10349   AIC:                         1.097e+04
Df Residuals:                   10345   BIC:                         1.100e+04
Df Model:                           3                                         
Covariance Type:            nonrobust                                         
====================================================================================
                       coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------------
Intercept            4.2977      0.006    775.432      0.000       4.287       4.309
np.log(age)          0.1825      0.000    506.667      0.000       0.182       0.183
np.log(vitaminc)    -0.0163      0.000    -43.304      0.000      -0.017      -0.016
np.log(zinc)        -0.0295      0.001    -19.829      0.000      -0.032      -0.027
==============================================================================
Omnibus:                    20976.764   Durbin-Watson:                   1.985
Prob(Omnibus):                  0.000   Jarque-Bera (JB):       1161624421.867
Skew:                         -15.502   Prob(JB):                         0.00
Kurtosis:                    1644.012   Cond. No.                     2.99e+03
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 2.99e+03. This might indicate that there are
strong multicollinearity or other numerical problems.

residuals = w_bpsystol_model.resid
fitted = w_bpsystol_model.fittedvalues

fig, axs = plt.subplots(2, 2, figsize=(20, 15))

sm.qqplot(residuals, line='s', ax=axs[0,0])
axs[0,0].set_title('QQ Plot of Residuals')

axs[0,1].scatter(fitted, residuals)
axs[0,1].axhline(y=0, color='red', linestyle='--')
axs[0,1].set_xlabel('Fitted Values')
axs[0,1].set_ylabel('Residuals')
axs[0,1].set_title('Residuals vs Fitted Values')

axs[1,0].hist(residuals, bins=15, edgecolor='black')
axs[1,0].set_title('Histogram of Residuals')

sns.boxplot(residuals, ax= axs[1,1])
axs[1,1].set_title('Boxplot of Residuals')

plt.tight_layout()
plt.show()

influence_5 = oi.OLSInfluence(w_bpsystol_model).summary_frame()
influence_5

k = len(w_bpsystol_model.params) - 1  # subtracting 1 for the intercept
n = len(num_nhanes)

# Thresholds
leverage_threshold = 3 * (k + 1) / n
cooks_d_threshold1 = 0.5  # Somewhat influential
cooks_d_threshold2 = 1    # Excessively influential

# Create subplots for each criterion
fig, axs = plt.subplots(1, 3, figsize=(18, 6))

# Studentized Residuals Plot
axs[0].scatter(range(n), influence_5["student_resid"])
axs[0].axhline(y=3, color='red', linestyle='--')
axs[0].axhline(y=-3, color='red', linestyle='--')
axs[0].set_xlabel('Observation')
axs[0].set_ylabel('Studentized Residuals')
axs[0].set_title('Studentized Residuals with ±3 Threshold')

# Leverage Plot
axs[1].scatter(range(n), influence_5["hat_diag"])
axs[1].axhline(y=leverage_threshold, color='red', linestyle='--')
axs[1].set_xlabel('Observation')
axs[1].set_ylabel('Leverage')
axs[1].set_title('Leverage Values with Threshold')

# Cook's Distance Plot
axs[2].stem(influence_5["cooks_d"])
axs[2].axhline(y=cooks_d_threshold1, color='orange', linestyle='--')
axs[2].axhline(y=cooks_d_threshold2, color='red', linestyle='--')
axs[2].set_xlabel('Observation')
axs[2].set_ylabel("Cook's Distance")
axs[2].set_title("Cook's Distance with Thresholds")

plt.tight_layout()
plt.show()

w_bpsystol_hetro = ssd.het_breuschpagan(w_bpsystol_model.resid,w_bpsystol_model.model.exog)
w_bpsystol_hetro_test_statistic, w_bpsystol_hetro_p_value = w_bpsystol_hetro[:2]
w_bpsystol_hetro_test_statistic, w_bpsystol_hetro_p_value

(142.98594152824862, 8.582031759436089e-31)

hct_model = smf.ols('(tcresult)~weight+age+sex+hdresult',data=nhanes).fit()

print(hct_model.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:               tcresult   R-squared:                       0.110
Model:                            OLS   Adj. R-squared:                  0.110
Method:                 Least Squares   F-statistic:                     319.8
Date:                Sun, 21 Jan 2024   Prob (F-statistic):          7.64e-260
Time:                        23:26:39   Log-Likelihood:                -48808.
No. Observations:               10349   AIC:                         9.763e+04
Df Residuals:                   10344   BIC:                         9.766e+04
Df Model:                           4                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
Intercept    169.5813      3.178     53.353      0.000     163.351     175.812
weight         0.2174      0.030      7.260      0.000       0.159       0.276
age            0.5243      0.015     33.873      0.000       0.494       0.555
sex           -4.3172      0.602     -7.172      0.000      -5.497      -3.137
hdresult       0.1465      0.039      3.782      0.000       0.071       0.222
==============================================================================
Omnibus:                      126.442   Durbin-Watson:                   2.012
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              112.413
Skew:                           0.206   Prob(JB):                     3.89e-25
Kurtosis:                       2.697   Cond. No.                     1.18e+03
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.18e+03. This might indicate that there are
strong multicollinearity or other numerical problems.

residuals = hct_model.resid
fitted = hct_model.fittedvalues

fig, axs = plt.subplots(2, 2, figsize=(20, 15))

sm.qqplot(residuals, line='s', ax=axs[0,0])
axs[0,0].set_title('QQ Plot of Residuals')

axs[0,1].scatter(fitted, residuals)
axs[0,1].axhline(y=0, color='red', linestyle='--')
axs[0,1].set_xlabel('Fitted Values')
axs[0,1].set_ylabel('Residuals')
axs[0,1].set_title('Residuals vs Fitted Values')

axs[1,0].hist(residuals, bins=15, edgecolor='black')
axs[1,0].set_title('Histogram of Residuals')

sns.boxplot(residuals, ax= axs[1,1])
axs[1,1].set_title('Boxplot of Residuals')

plt.tight_layout()
plt.show()

influence_6 = oi.OLSInfluence(hct_model).summary_frame()
influence_6

k = len(hct_model.params) - 1  # subtracting 1 for the intercept
n = len(num_nhanes)

# Thresholds
leverage_threshold = 3 * (k + 1) / n
cooks_d_threshold1 = 0.5  # Somewhat influential
cooks_d_threshold2 = 1    # Excessively influential

# Create subplots for each criterion
fig, axs = plt.subplots(1, 3, figsize=(18, 6))

# Studentized Residuals Plot
axs[0].scatter(range(n), influence_6["student_resid"])
axs[0].axhline(y=3, color='red', linestyle='--')
axs[0].axhline(y=-3, color='red', linestyle='--')
axs[0].set_xlabel('Observation')
axs[0].set_ylabel('Studentized Residuals')
axs[0].set_title('Studentized Residuals with ±3 Threshold')

# Leverage Plot
axs[1].scatter(range(n), influence_6["hat_diag"])
axs[1].axhline(y=leverage_threshold, color='red', linestyle='--')
axs[1].set_xlabel('Observation')
axs[1].set_ylabel('Leverage')
axs[1].set_title('Leverage Values with Threshold')

# Cook's Distance Plot
axs[2].stem(influence_6["cooks_d"])
axs[2].axhline(y=cooks_d_threshold1, color='orange', linestyle='--')
axs[2].axhline(y=cooks_d_threshold2, color='red', linestyle='--')
axs[2].set_xlabel('Observation')
axs[2].set_ylabel("Cook's Distance")
axs[2].set_title("Cook's Distance with Thresholds")

plt.tight_layout()
plt.show()

hct_hetro = ssd.het_breuschpagan(hct_model.resid,hct_model.model.exog)
hct_hetro_test_statistic, hct_hetro_p_value = hct_hetro[:2]
hct_hetro_test_statistic, hct_hetro_p_value

(42.69358138961119, 1.1979032859246492e-08)

hct_model_t = smf.ols('np.log(tcresult)~weight+age+sex+hdresult',data=nhanes).fit()

print(hct_model_t.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:       np.log(tcresult)   R-squared:                       0.111
Model:                            OLS   Adj. R-squared:                  0.111
Method:                 Least Squares   F-statistic:                     323.1
Date:                Sun, 21 Jan 2024   Prob (F-statistic):          1.99e-262
Time:                        23:27:05   Log-Likelihood:                 6748.9
No. Observations:               10349   AIC:                        -1.349e+04
Df Residuals:                   10344   BIC:                        -1.345e+04
Df Model:                           4                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
Intercept      5.1491      0.015    347.510      0.000       5.120       5.178
weight         0.0010      0.000      7.396      0.000       0.001       0.001
age            0.0025   7.22e-05     34.068      0.000       0.002       0.003
sex           -0.0201      0.003     -7.146      0.000      -0.026      -0.015
hdresult       0.0007      0.000      3.650      0.000       0.000       0.001
==============================================================================
Omnibus:                       97.895   Durbin-Watson:                   2.013
Prob(Omnibus):                  0.000   Jarque-Bera (JB):               67.714
Skew:                          -0.073   Prob(JB):                     1.98e-15
Kurtosis:                       2.632   Cond. No.                     1.18e+03
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.18e+03. This might indicate that there are
strong multicollinearity or other numerical problems.

residuals = hct_model_t.resid
fitted = hct_model_t.fittedvalues

fig, axs = plt.subplots(2, 2, figsize=(20, 15))

sm.qqplot(residuals, line='s', ax=axs[0,0])
axs[0,0].set_title('QQ Plot of Residuals')

axs[0,1].scatter(fitted, residuals)
axs[0,1].axhline(y=0, color='red', linestyle='--')
axs[0,1].set_xlabel('Fitted Values')
axs[0,1].set_ylabel('Residuals')
axs[0,1].set_title('Residuals vs Fitted Values')

axs[1,0].hist(residuals, bins=15, edgecolor='black')
axs[1,0].set_title('Histogram of Residuals')

sns.boxplot(residuals, ax= axs[1,1])
axs[1,1].set_title('Boxplot of Residuals')

plt.tight_layout()
plt.show()

influence_7 = oi.OLSInfluence(hct_model_t).summary_frame()
influence_7

k = len(hct_model_t.params) - 1  # subtracting 1 for the intercept
n = len(num_nhanes)

# Thresholds
leverage_threshold = 3 * (k + 1) / n
cooks_d_threshold1 = 0.5  # Somewhat influential
cooks_d_threshold2 = 1    # Excessively influential

# Create subplots for each criterion
fig, axs = plt.subplots(1, 3, figsize=(18, 6))

# Studentized Residuals Plot
axs[0].scatter(range(n), influence_7["student_resid"])
axs[0].axhline(y=3, color='red', linestyle='--')
axs[0].axhline(y=-3, color='red', linestyle='--')
axs[0].set_xlabel('Observation')
axs[0].set_ylabel('Studentized Residuals')
axs[0].set_title('Studentized Residuals with ±3 Threshold')

# Leverage Plot
axs[1].scatter(range(n), influence_7["hat_diag"])
axs[1].axhline(y=leverage_threshold, color='red', linestyle='--')
axs[1].set_xlabel('Observation')
axs[1].set_ylabel('Leverage')
axs[1].set_title('Leverage Values with Threshold')

# Cook's Distance Plot
axs[2].stem(influence_7["cooks_d"])
axs[2].axhline(y=cooks_d_threshold1, color='orange', linestyle='--')
axs[2].axhline(y=cooks_d_threshold2, color='red', linestyle='--')
axs[2].set_xlabel('Observation')
axs[2].set_ylabel("Cook's Distance")
axs[2].set_title("Cook's Distance with Thresholds")

plt.tight_layout()
plt.show()

hct_hetro_t = ssd.het_breuschpagan(hct_model_t.resid,hct_model_t.model.exog)
hct_hetro_t_test_statistic, hct_hetro_t_p_value = hct_hetro_t[:2]
print(hct_hetro_t_test_statistic, hct_hetro_t_p_value)

13.529569280961393 0.008958200413191092

weight =1/(bpsystol_model.resid**2)

w_hct_model=smf.wls('(tcresult)~weight+age+sex+hdresult',data=nhanes,weights=waight).fit()

w_hct_model.summary()

residuals = w_hct_model.resid
fitted = w_hct_model.fittedvalues

fig, axs = plt.subplots(2, 2, figsize=(20, 15))

sm.qqplot(residuals, line='s', ax=axs[0,0])
axs[0,0].set_title('QQ Plot of Residuals')

axs[0,1].scatter(fitted, residuals)
axs[0,1].axhline(y=0, color='red', linestyle='--')
axs[0,1].set_xlabel('Fitted Values')
axs[0,1].set_ylabel('Residuals')
axs[0,1].set_title('Residuals vs Fitted Values')

axs[1,0].hist(residuals, bins=15, edgecolor='black')
axs[1,0].set_title('Histogram of Residuals')

sns.boxplot(residuals, ax= axs[1,1])
axs[1,1].set_title('Boxplot of Residuals')

plt.tight_layout()
plt.show()

influence_8 = oi.OLSInfluence(w_hct_model).summary_frame()
influence_8

k = len(w_hct_model.params) - 1  # subtracting 1 for the intercept
n = len(num_nhanes)

# Thresholds
leverage_threshold = 3 * (k + 1) / n
cooks_d_threshold1 = 0.5  # Somewhat influential
cooks_d_threshold2 = 1    # Excessively influential

# Create subplots for each criterion
fig, axs = plt.subplots(1, 3, figsize=(18, 6))

# Studentized Residuals Plot
axs[0].scatter(range(n), influence_8["student_resid"])
axs[0].axhline(y=3, color='red', linestyle='--')
axs[0].axhline(y=-3, color='red', linestyle='--')
axs[0].set_xlabel('Observation')
axs[0].set_ylabel('Studentized Residuals')
axs[0].set_title('Studentized Residuals with ±3 Threshold')

# Leverage Plot
axs[1].scatter(range(n), influence_8["hat_diag"])
axs[1].axhline(y=leverage_threshold, color='red', linestyle='--')
axs[1].set_xlabel('Observation')
axs[1].set_ylabel('Leverage')
axs[1].set_title('Leverage Values with Threshold')

# Cook's Distance Plot
axs[2].stem(influence_8["cooks_d"])
axs[2].axhline(y=cooks_d_threshold1, color='orange', linestyle='--')
axs[2].axhline(y=cooks_d_threshold2, color='red', linestyle='--')
axs[2].set_xlabel('Observation')
axs[2].set_ylabel("Cook's Distance")
axs[2].set_title("Cook's Distance with Thresholds")

plt.tight_layout()
plt.show()

w_hct_hetro = ssd.het_breuschpagan(w_hct_model.resid,w_hct_model.model.exog)
w_hct_hetro_test_statistic, w_hct_hetro_p_value = w_hct_hetro[:2]
w_hct_hetro_test_statistic, w_hct_hetro_p_value

(156.28101533760918, 9.170806669820822e-33)

w_hct_model_t=smf.wls('np.log(tcresult)~weight+age+sex+hdresult',data=nhanes,weights=waight).fit()

print(w_hct_model_t.summary())

                            WLS Regression Results                            
==============================================================================
Dep. Variable:       np.log(tcresult)   R-squared:                       0.947
Model:                            WLS   Adj. R-squared:                  0.947
Method:                 Least Squares   F-statistic:                 4.655e+04
Date:                Sun, 21 Jan 2024   Prob (F-statistic):               0.00
Time:                        23:27:57   Log-Likelihood:                -27779.
No. Observations:               10349   AIC:                         5.557e+04
Df Residuals:                   10344   BIC:                         5.560e+04
Df Model:                           4                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
Intercept      5.0225      0.021    242.731      0.000       4.982       5.063
weight        -0.0047      0.000    -31.596      0.000      -0.005      -0.004
age           -0.0017   2.93e-05    -58.692      0.000      -0.002      -0.002
sex            0.0500      0.001     51.436      0.000       0.048       0.052
hdresult       0.0152      0.000     63.621      0.000       0.015       0.016
==============================================================================
Omnibus:                    27150.687   Durbin-Watson:                   1.999
Prob(Omnibus):                  0.000   Jarque-Bera (JB):       2674813196.118
Skew:                         -29.942   Prob(JB):                         0.00
Kurtosis:                    2492.875   Cond. No.                     2.07e+04
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 2.07e+04. This might indicate that there are
strong multicollinearity or other numerical problems.

residuals = w_hct_model_t.resid
fitted = w_hct_model_t.fittedvalues

fig, axs = plt.subplots(2, 2, figsize=(20, 15))

sm.qqplot(residuals, line='s', ax=axs[0,0])
axs[0,0].set_title('QQ Plot of Residuals')

axs[0,1].scatter(fitted, residuals)
axs[0,1].axhline(y=0, color='red', linestyle='--')
axs[0,1].set_xlabel('Fitted Values')
axs[0,1].set_ylabel('Residuals')
axs[0,1].set_title('Residuals vs Fitted Values')

axs[1,0].hist(residuals, bins=15, edgecolor='black')
axs[1,0].set_title('Histogram of Residuals')

sns.boxplot(residuals, ax= axs[1,1])
axs[1,1].set_title('Boxplot of Residuals')

plt.tight_layout()
plt.show()

influence_9 = oi.OLSInfluence(w_hct_model_t).summary_frame()
influence_9

k = len(w_hct_model_t.params) - 1  # subtracting 1 for the intercept
n = len(num_nhanes)

# Thresholds
leverage_threshold = 3 * (k + 1) / n
cooks_d_threshold1 = 0.5  # Somewhat influential
cooks_d_threshold2 = 1    # Excessively influential

# Create subplots for each criterion
fig, axs = plt.subplots(1, 3, figsize=(18, 6))

# Studentized Residuals Plot
axs[0].scatter(range(n), influence_9["student_resid"])
axs[0].axhline(y=3, color='red', linestyle='--')
axs[0].axhline(y=-3, color='red', linestyle='--')
axs[0].set_xlabel('Observation')
axs[0].set_ylabel('Studentized Residuals')
axs[0].set_title('Studentized Residuals with ±3 Threshold')

# Leverage Plot
axs[1].scatter(range(n), influence_9["hat_diag"])
axs[1].axhline(y=leverage_threshold, color='red', linestyle='--')
axs[1].set_xlabel('Observation')
axs[1].set_ylabel('Leverage')
axs[1].set_title('Leverage Values with Threshold')

# Cook's Distance Plot
axs[2].stem(influence_9["cooks_d"])
axs[2].axhline(y=cooks_d_threshold1, color='orange', linestyle='--')
axs[2].axhline(y=cooks_d_threshold2, color='red', linestyle='--')
axs[2].set_xlabel('Observation')
axs[2].set_ylabel("Cook's Distance")
axs[2].set_title("Cook's Distance with Thresholds")

plt.tight_layout()
plt.show()

w_hct_hetro_t = ssd.het_breuschpagan(w_hct_model_t.resid,w_hct_model_t.model.exog)
w_hct_hetro_t_test_statistic, w_hct_hetro_t_p_value = w_hct_hetro_t[:2]
w_hct_hetro_t_test_statistic, w_hct_hetro_t_p_value

(282.97190630255824, 5.09569389536182e-60)

diabetes_model = smf.logit('(heartatk)~age+sex+weight',data=nhanes).fit()

Optimization terminated successfully.
         Current function value: 0.157190
         Iterations 9

print(diabetes_model.summary())

                           Logit Regression Results                           
==============================================================================
Dep. Variable:               heartatk   No. Observations:                10349
Model:                          Logit   Df Residuals:                    10345
Method:                           MLE   Df Model:                            3
Date:                Sun, 21 Jan 2024   Pseudo R-squ.:                  0.1574
Time:                        23:28:28   Log-Likelihood:                -1626.8
converged:                       True   LL-Null:                       -1930.6
Covariance Type:            nonrobust   LLR p-value:                2.189e-131
==============================================================================
                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
Intercept     -8.5201      0.495    -17.200      0.000      -9.491      -7.549
age            0.0857      0.005     17.508      0.000       0.076       0.095
sex            0.8990      0.110      8.207      0.000       0.684       1.114
weight         0.0015      0.005      0.292      0.771      -0.009       0.012
==============================================================================

tcresult_model = smf.ols('(bmi)~hlthstat',data=nhanes).fit()
print(tcresult_model.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:                    bmi   R-squared:                       0.015
Model:                            OLS   Adj. R-squared:                  0.015
Method:                 Least Squares   F-statistic:                     31.69
Date:                Sun, 21 Jan 2024   Prob (F-statistic):           3.74e-32
Time:                        23:28:28   Log-Likelihood:                -26459.
No. Observations:               10349   AIC:                         5.293e+04
Df Residuals:                   10343   BIC:                         5.297e+04
Df Model:                           5                                         
Covariance Type:            nonrobust                                         
=========================================================================================
                            coef    std err          t      P>|t|      [0.025      0.975]
-----------------------------------------------------------------------------------------
Intercept                24.0620      0.834     28.852      0.000      22.427      25.697
hlthstat[T.Excellent]     0.5345      0.836      0.639      0.523      -1.105       2.174
hlthstat[T.Fair]          1.6234      0.837      1.938      0.053      -0.018       3.265
hlthstat[T.Good]          1.2972      0.836      1.552      0.121      -0.341       2.936
hlthstat[T.Poor]          1.3981      0.842      1.661      0.097      -0.252       3.048
hlthstat[T.Very good]     0.8783      0.836      1.050      0.294      -0.761       2.518
==============================================================================
Omnibus:                      146.673   Durbin-Watson:                   2.009
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              152.226
Skew:                           0.294   Prob(JB):                     8.80e-34
Kurtosis:                       2.908   Cond. No.                         74.0
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

av.anova_lm(tcresult_model)

tcresult_model_a = smf.ols('(bmi)~hlthstat+weight',data=nhanes).fit()
print(tcresult_model_a.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:                    bmi   R-squared:                       0.550
Model:                            OLS   Adj. R-squared:                  0.550
Method:                 Least Squares   F-statistic:                     2105.
Date:                Sun, 21 Jan 2024   Prob (F-statistic):               0.00
Time:                        23:28:28   Log-Likelihood:                -22407.
No. Observations:               10349   AIC:                         4.483e+04
Df Residuals:                   10342   BIC:                         4.488e+04
Df Model:                           6                                         
Covariance Type:            nonrobust                                         
=========================================================================================
                            coef    std err          t      P>|t|      [0.025      0.975]
-----------------------------------------------------------------------------------------
Intercept                 8.8474      0.580     15.246      0.000       7.710       9.985
hlthstat[T.Excellent]    -0.2614      0.566     -0.462      0.644      -1.370       0.847
hlthstat[T.Fair]          0.8022      0.566      1.417      0.157      -0.308       1.912
hlthstat[T.Good]          0.4710      0.565      0.833      0.405      -0.637       1.579
hlthstat[T.Poor]          0.6074      0.569      1.067      0.286      -0.508       1.723
hlthstat[T.Very good]     0.1107      0.565      0.196      0.845      -0.998       1.219
weight                    0.2260      0.002    110.841      0.000       0.222       0.230
==============================================================================
Omnibus:                       69.546   Durbin-Watson:                   1.973
Prob(Omnibus):                  0.000   Jarque-Bera (JB):               70.840
Skew:                           0.201   Prob(JB):                     4.14e-16
Kurtosis:                       2.953   Cond. No.                     4.77e+03
==============================================================================

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 4.77e+03. This might indicate that there are
strong multicollinearity or other numerical problems.

av.anova_lm(tcresult_model_a)

	sampl	strata	location	height	weight	tcresult	hdresult	hgb	hct	tibc	...	smsa_all	region_all	sex	race	diabetes	hlthstat	sizplace
0	33576.600295	15.942383	32.942435	174.598007	62.480000	226.000000	50.674981	13.900000	42.700001	377.0	...	2	3	1	0	0	Very good	Urbanized area; 1,000,000–2,999,999
1	33759.234650	16.451747	33.194070	166.820595	58.390811	179.000000	56.752631	13.756261	40.947136	363.0	...	2	3	0	0	0	Very good	Urbanized area; 1,000,000–2,999,999
2	33937.406792	16.611585	33.269093	164.098007	67.250000	218.679905	57.298683	13.500000	40.500000	353.0	...	1	3	0	2	0	Good	Urbanized area; 1,000,000–2,999,999
3	33732.309667	16.701131	33.170338	162.598007	67.465754	189.000000	41.660850	13.400000	38.700001	365.0	...	2	3	0	0	1	Fair	Urbanized area; 1,000,000–2,999,999
4	33695.912447	17.384561	33.063440	163.098007	74.279999	226.440007	48.591742	15.600000	45.500000	320.0	...	1	3	0	0	0	Very good	Urbanized area; 1,000,000–2,999,999

	sampl	strata	location	height	weight	tcresult	hdresult	hgb	hct	tibc	...	hsizgp	highbp	smsa_all	region_all	psu	sex	race	heartatk	diabetes	rural
count	10349.000000	10349.000000	10349.000000	10349.000000	10349.000000	10349.000000	10349.000000	10349.000000	10349.000000	10349.000000	...	10349.000000	10349.000000	10349.000000	10349.000000	10349.000000	10349.000000	10349.000000	10349.000000	10349.000000	10349.000000
mean	33745.987697	17.031454	33.183235	167.853916	70.861242	215.006209	48.628920	14.270329	42.014210	363.349423	...	2.790608	0.422843	2.200792	2.581119	0.481882	0.474925	0.143589	0.045995	0.048217	0.367378
std	13382.840533	7.422151	13.382768	8.334846	10.172868	28.664102	7.412772	0.927888	2.429586	45.413194	...	1.331985	0.494035	0.818039	1.075303	0.499696	0.499395	0.402042	0.209484	0.214235	0.482114
min	7465.000000	4.000000	7.000000	136.796996	46.930409	160.000000	35.000000	12.347565	36.845788	106.961345	...	1.000000	0.000000	1.000000	1.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
25%	25490.000000	11.000000	25.000000	161.699005	63.160000	195.000000	43.632958	13.600000	40.000000	333.000000	...	2.000000	0.000000	1.000000	2.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
50%	33761.650423	17.000000	33.189348	167.500000	70.080002	214.000000	48.144409	14.296057	42.000000	361.000000	...	2.000000	0.000000	2.000000	3.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
75%	43563.000000	23.000000	43.000000	173.891380	78.360001	233.000000	53.000000	15.000000	44.000000	393.000000	...	4.000000	1.000000	3.000000	4.000000	1.000000	1.000000	0.000000	0.000000	0.000000	1.000000
max	57720.000000	30.000000	57.000000	198.415589	99.727269	282.000000	66.000000	16.232429	47.158331	580.102639	...	5.000000	1.000000	3.000000	4.000000	1.000000	1.000000	2.000000	1.000000	1.000000	1.000000

	dfb_Intercept	dfb_height	dfb_weight	cooks_d	standard_resid	hat_diag	dffits_internal	student_resid	dffits
0	-0.024296	0.033923	-0.034113	6.847282e-04	2.360127	0.000369	0.045323	2.360649	0.045333
1	-0.000121	0.000652	-0.001452	1.086317e-06	0.108228	0.000278	0.001805	0.108223	0.001805
2	-0.000189	0.000127	0.000057	6.839869e-08	-0.041679	0.000118	-0.000453	-0.041677	-0.000453
3	0.000429	-0.000345	-0.000001	1.941115e-07	0.065660	0.000135	0.000763	0.065657	0.000763
4	0.006464	-0.007465	0.006355	4.532443e-05	0.863756	0.000182	0.011661	0.863745	0.011661
...	...	...	...	...	...	...	...	...	...
10344	0.000351	-0.002241	0.005194	1.275918e-05	-0.336831	0.000337	-0.006187	-0.336816	-0.006187
10345	0.001795	-0.001493	0.000041	2.282837e-06	0.199584	0.000172	0.002617	0.199575	0.002617
10346	0.001764	-0.001864	0.001314	4.170701e-06	0.303203	0.000136	0.003537	0.303190	0.003537
10347	-0.000238	0.000795	-0.001601	1.082621e-06	0.084047	0.000460	0.001802	0.084043	0.001802
10348	0.000082	-0.000124	0.000143	1.009400e-08	-0.008194	0.000451	-0.000174	-0.008194	-0.000174

	dfb_Intercept	dfb_np.log(height)	dfb_np.log(weight)	cooks_d	standard_resid	hat_diag	dffits_internal	student_resid	dffits
0	0.000076	-0.000095	0.000095	5.385526e-09	-0.006672	0.000363	-0.000127	-0.006671	-0.000127
1	-0.000552	0.001315	-0.002831	3.986592e-06	0.201017	0.000296	0.003458	0.201007	0.003458
2	0.000218	-0.000176	-0.000042	1.159711e-07	0.054970	0.000115	0.000590	0.054968	0.000590
3	0.000410	-0.000369	0.000041	2.026473e-07	0.067454	0.000134	0.000780	0.067451	0.000780
4	0.000714	-0.000841	0.000760	5.766591e-07	0.095556	0.000189	0.001315	0.095551	0.001315
...	...	...	...	...	...	...	...	...	...
10344	0.000055	-0.000140	0.000313	4.426029e-08	-0.018821	0.000375	-0.000364	-0.018820	-0.000364
10345	0.001270	-0.001146	0.000120	1.244329e-06	0.147494	0.000172	0.001932	0.147487	0.001932
10346	-0.000052	0.000058	-0.000046	3.983219e-09	-0.009219	0.000141	-0.000109	-0.009218	-0.000109
10347	-0.000308	0.000638	-0.001258	6.429673e-07	0.059721	0.000541	0.001389	0.059718	0.001389
10348	0.026411	-0.035202	0.040716	8.090136e-04	-2.284727	0.000465	-0.049265	-2.285193	-0.049275

	dfb_Intercept	dfb_height	dfb_weight	cooks_d	standard_resid	hat_diag	dffits_internal	student_resid	dffits
0	-40.784084	51.389516	-35.840255	4.669999e-11	0.377658	9.822918e-10	1.183638e-05	2.360122	0.000074
1	-4.348674	6.166194	-5.185600	1.431844e-12	0.017309	1.433797e-08	2.072566e-06	0.108139	0.000013
2	-4.451086	5.452530	-3.769255	1.443560e-13	-0.006672	9.727042e-09	-6.580790e-07	-0.041688	-0.000004
3	-3.520865	4.810355	-3.823900	1.940303e-13	0.010508	5.272005e-09	7.629489e-07	0.065649	0.000005
4	5.574361	-4.866353	2.141968	6.272926e-12	0.138237	9.847879e-10	4.338062e-06	0.863692	0.000027
...	...	...	...	...	...	...	...	...	...
10344	-3.638345	2.233110	1.051895	5.462373e-12	-0.053913	5.637811e-09	-4.048101e-06	-0.336835	-0.000025
10345	-1.461660	3.249956	-3.784476	4.914107e-13	0.031941	1.444971e-09	1.214180e-06	0.199560	0.000008
10346	-1.508898	2.746575	-2.588856	1.584662e-12	0.048527	2.018824e-09	2.180364e-06	0.303180	0.000014
10347	-4.525293	6.360859	-5.324704	1.951968e-12	0.013434	3.244737e-08	2.419897e-06	0.083932	0.000015
10348	-4.043562	5.110964	-3.688199	1.997531e-13	-0.001327	3.400872e-07	-7.741183e-07	-0.008293	-0.000005

intro¶

Objectives¶

questions¶

1- Descriptive questions¶

2- Exploratory questions¶

3-predictive question¶

Analysis¶

descrptive analysis¶

exploratory analysis¶

bmi model¶

transformation¶

Weight least squaren bmi model¶

transformation¶

logestic highbp model¶

bpsystol_model¶

weight¶

hct_model¶

transformation¶

weight¶

wtransformation¶

diabetes_logistic_model¶

ANOVA¶

Dep. Variable:	np.log(bmi)	R-squared:	0.995
Model:	OLS	Adj. R-squared:	0.995
Method:	Least Squares	F-statistic:	9.375e+05
Date:	Sun, 21 Jan 2024	Prob (F-statistic):	0.00
Time:	23:23:58	Log-Likelihood:	33777.
No. Observations:	10349	AIC:	-6.755e+04
Df Residuals:	10346	BIC:	-6.753e+04
Df Model:	2
Covariance Type:	nonrobust

	coef	std err	t	P>\|t\|	[0.025	0.975]
Intercept	9.1985	0.010	944.891	0.000	9.179	9.218
np.log(height)	-1.9949	0.002	-928.220	0.000	-1.999	-1.991
np.log(weight)	0.9965	0.001	1343.721	0.000	0.995	0.998

Omnibus:	2391.889	Durbin-Watson:	2.020
Prob(Omnibus):	0.000	Jarque-Bera (JB):	23731.596
Skew:	-0.824	Prob(JB):	0.00
Kurtosis:	10.233	Cond. No.	737.

Dep. Variable:	bmi	R-squared:	1.000
Model:	WLS	Adj. R-squared:	1.000
Method:	Least Squares	F-statistic:	5.554e+10
Date:	Sun, 21 Jan 2024	Prob (F-statistic):	0.00
Time:	23:24:28	Log-Likelihood:	17984.
No. Observations:	10349	AIC:	-3.596e+04
Df Residuals:	10346	BIC:	-3.594e+04
Df Model:	2
Covariance Type:	nonrobust

Omnibus:	35613.664	Durbin-Watson:	2.010
Prob(Omnibus):	0.000	Jarque-Bera (JB):	1724.532
Skew:	-0.032	Prob(JB):	0.00
Kurtosis:	1.001	Cond. No.	3.52e+03

Omnibus:	18627.321	Durbin-Watson:	2.007
Prob(Omnibus):	0.000	Jarque-Bera (JB):	125936881.791
Skew:	-12.367	Prob(JB):	0.00
Kurtosis:	542.856	Cond. No.	716.

	dfb_Intercept	dfb_np.log(height)	dfb_np.log(weight)	cooks_d	standard_resid	hat_diag	dffits_internal	student_resid	dffits
0	-43411.712078	48523.623092	-27946.069551	5.539883e-16	-0.001364	8.927976e-10	-4.076720e-08	-0.742166	-0.000022
1	-43412.752443	48525.762478	-27949.018569	1.803693e-15	-0.000613	1.439522e-08	-7.356005e-08	-0.333504	-0.000040
2	-43411.503272	48523.512698	-27946.208721	1.134050e-17	-0.000059	9.925647e-09	-5.832795e-09	-0.031847	-0.000003
3	-43411.213994	48523.236610	-27946.128528	2.168976e-17	0.000109	5.480426e-09	8.066554e-09	0.059272	0.000004
4	-43410.762584	48522.563759	-27945.424069	8.910846e-17	0.000517	9.995888e-10	1.635009e-08	0.281304	0.000009
...	...	...	...	...	...	...	...	...	...
10344	-43411.744798	48523.558982	-27945.854390	2.503093e-15	-0.001128	5.899438e-09	-8.665610e-08	-0.613706	-0.000047
10345	-43409.942787	48522.151293	-27946.073738	6.785364e-17	0.000370	1.485505e-09	1.426748e-08	0.201362	0.000008
10346	-43411.907262	48523.845872	-27946.208971	1.150995e-17	0.000128	2.121744e-09	5.876210e-09	0.069393	0.000003
10347	-43412.304701	48524.694272	-27947.412895	1.873040e-14	-0.001258	3.549568e-08	-2.370468e-07	-0.684405	-0.000129
10348	-43382.633464	48484.981479	-27912.934732	3.467646e-12	-0.005702	3.199563e-07	-3.225358e-06	-3.102480	-0.001755

Dep. Variable:	bpsystol	R-squared:	0.235
Model:	OLS	Adj. R-squared:	0.235
Method:	Least Squares	F-statistic:	1059.
Date:	Sun, 21 Jan 2024	Prob (F-statistic):	0.00
Time:	23:25:34	Log-Likelihood:	-45896.
No. Observations:	10349	AIC:	9.180e+04
Df Residuals:	10345	BIC:	9.183e+04
Df Model:	3
Covariance Type:	nonrobust

Omnibus:	1507.947	Durbin-Watson:	1.881
Prob(Omnibus):	0.000	Jarque-Bera (JB):	3290.606
Skew:	0.868	Prob(JB):	0.00
Kurtosis:	5.148	Cond. No.	1.14e+03

	dfb_Intercept	dfb_age	dfb_vitaminc	dfb_zinc	cooks_d	standard_resid	hat_diag	dffits_internal	student_resid	dffits
0	0.027046	-0.010737	0.023627	-0.033641	0.000483	-1.509598	0.000848	-0.043970	-1.509691	-0.043973
1	-0.002470	0.003906	-0.005069	0.002081	0.000029	-0.873989	0.000150	-0.010702	-0.873979	-0.010702
2	0.009813	0.009693	-0.006355	-0.012246	0.000086	-0.681574	0.000738	-0.018523	-0.681556	-0.018523
3	0.001759	0.015960	0.004011	-0.005289	0.000172	1.925351	0.000186	0.026258	1.925603	0.026262
4	0.018464	-0.010142	-0.007061	-0.016527	0.000127	-0.993609	0.000513	-0.022502	-0.993608	-0.022502
...	...	...	...	...	...	...	...	...	...	...
10344	-0.003172	0.009130	0.002175	-0.000710	0.000066	-1.318077	0.000151	-0.016211	-1.318124	-0.016212
10345	0.000159	-0.012534	0.008959	0.002262	0.000108	1.445952	0.000207	0.020799	1.446028	0.020800
10346	0.001417	-0.002023	0.000768	-0.001432	0.000003	-0.258941	0.000186	-0.003533	-0.258930	-0.003533
10347	-0.000618	0.007422	-0.000880	-0.001722	0.000028	-0.713046	0.000217	-0.010495	-0.713029	-0.010495
10348	0.005441	0.006755	0.014006	-0.011984	0.000129	-0.971789	0.000544	-0.022677	-0.971786	-0.022677

	coef	std err	t	P>\|t\|	[0.025	0.975]
Intercept	105.1161	2.309	45.517	0.000	100.589	109.643
age	0.6581	0.012	55.990	0.000	0.635	0.681
vitaminc	-3.5798	0.527	-6.792	0.000	-4.613	-2.547
zinc	-0.0233	0.025	-0.939	0.348	-0.072	0.025

	dfb_Intercept	dfb_np.log(age)	dfb_np.log(vitaminc)	dfb_np.log(zinc)	cooks_d	standard_resid	hat_diag	dffits_internal	student_resid	dffits
0	7.225336	-14.488320	1.137714	-3.065438	3.230234e-05	-5.855254	3.768780e-06	-0.011367	-1.601901	-0.003110
1	7.088845	-14.443231	1.056563	-2.960744	5.162824e-06	-3.888474	1.365804e-06	-0.004544	-1.063738	-0.001243
2	7.131869	-14.413183	1.055594	-3.002732	8.701761e-06	-3.111063	3.596235e-06	-0.005900	-0.851047	-0.001614
3	7.104529	-14.411814	1.086088	-2.978457	1.977301e-05	6.611814	1.809217e-06	0.008893	1.808916	0.002433
4	7.153534	-14.475310	1.056786	-3.008142	3.022189e-06	-3.154349	1.214959e-06	-0.003477	-0.862899	-0.000951
...	...	...	...	...	...	...	...	...	...	...
10344	7.097440	-14.426057	1.069873	-2.971744	4.188338e-07	-6.148481	4.431656e-08	-0.001294	-1.682123	-0.000354
10345	7.095902	-14.479773	1.093000	-2.957418	7.312139e-07	5.119681	1.115883e-07	0.001710	1.400614	0.000468
10346	7.101179	-14.452781	1.071591	-2.968460	1.114835e-07	-0.390292	2.927455e-06	-0.000668	-0.106763	-0.000183
10347	7.099534	-14.426039	1.065625	-2.973044	6.574337e-07	-3.302493	2.411172e-07	-0.001622	-0.903419	-0.000444
10348	7.141427	-14.430195	1.115477	-3.007100	3.836388e-05	-4.374055	8.020669e-06	-0.012388	-1.196590	-0.003389

	dfb_Intercept	dfb_weight	dfb_age	dfb_sex	dfb_hdresult	cooks_d	standard_resid	hat_diag	dffits_internal	student_resid	dffits
0	0.002357	-0.005561	0.001844	0.006660	0.001141	1.523537e-05	0.422253	0.000427	0.008728	0.422237	0.008728
1	-0.003247	0.008394	0.004472	0.004128	-0.008049	9.502283e-05	-1.223488	0.000317	-0.021797	-1.223518	-0.021798
2	-0.001930	0.002127	-0.008763	-0.003989	0.005665	3.247657e-05	0.557489	0.000522	0.012743	0.557471	0.012743
3	-0.011782	0.003444	-0.011721	0.013717	0.016736	1.402158e-04	-1.271461	0.000433	-0.026478	-1.271499	-0.026479
4	-0.000006	0.000010	0.000013	-0.000017	-0.000002	1.324434e-10	0.001411	0.000332	0.000026	0.001411	0.000026
...	...	...	...	...	...	...	...	...	...	...	...
10344	-0.007661	0.008644	0.005718	0.003046	-0.000684	5.066214e-05	-0.848642	0.000352	-0.015916	-0.848630	-0.015916
10345	0.007862	-0.001854	-0.004090	-0.005849	-0.007961	2.675914e-05	0.525604	0.000484	0.011567	0.525586	0.011567
10346	-0.008713	-0.000857	-0.006114	0.011474	0.015178	8.163877e-05	-0.819373	0.000608	-0.020204	-0.819360	-0.020203
10347	-0.005697	0.011657	0.011145	0.001098	-0.009535	1.285314e-04	-1.076778	0.000554	-0.025351	-1.076787	-0.025351
10348	0.001739	-0.002707	-0.001476	0.002894	0.000492	3.454927e-06	0.171485	0.000587	0.004156	0.171477	0.004156

	dfb_Intercept	dfb_weight	dfb_age	dfb_sex	dfb_hdresult	cooks_d	standard_resid	hat_diag	dffits_internal	student_resid	dffits
0	0.002694	-0.006355	0.002107	0.007612	0.001304	1.989756e-05	0.482555	0.000427	0.009974	0.482537	0.009974
1	-0.003372	0.008719	0.004646	0.004288	-0.008360	1.025199e-04	-1.270837	0.000317	-0.022641	-1.270875	-0.022641
2	-0.002188	0.002412	-0.009936	-0.004522	0.006423	4.175154e-05	0.632103	0.000522	0.014448	0.632084	0.014448
3	-0.011714	0.003424	-0.011653	0.013637	0.016639	1.385895e-04	-1.264066	0.000433	-0.026324	-1.264102	-0.026325
4	-0.000239	0.000417	0.000520	-0.000685	-0.000085	2.249150e-07	0.058158	0.000332	0.001060	0.058156	0.001060
...	...	...	...	...	...	...	...	...	...	...	...
10344	-0.007728	0.008719	0.005768	0.003073	-0.000690	5.155278e-05	-0.856069	0.000352	-0.016055	-0.856058	-0.016055
10345	0.008874	-0.002093	-0.004616	-0.006602	-0.008986	3.408842e-05	0.593234	0.000484	0.013055	0.593215	0.013055
10346	-0.008201	-0.000807	-0.005755	0.010800	0.014286	7.233224e-05	-0.771257	0.000608	-0.019017	-0.771242	-0.019017
10347	-0.006057	0.012394	0.011849	0.001168	-0.010137	1.452855e-04	-1.144809	0.000554	-0.026952	-1.144826	-0.026953
10348	0.002436	-0.003793	-0.002068	0.004055	0.000689	6.780275e-06	0.240232	0.000587	0.005822	0.240221	0.005822

Omnibus:	24853.230	Durbin-Watson:	1.999
Prob(Omnibus):	0.000	Jarque-Bera (JB):	2004389488.810
Skew:	-23.717	Prob(JB):	0.00
Kurtosis:	2158.472	Cond. No.	2.07e+04

	dfb_Intercept	dfb_weight	dfb_age	dfb_sex	dfb_hdresult	cooks_d	standard_resid	hat_diag	dffits_internal	student_resid	dffits
0	-40.137434	-71.321982	-390.637967	156.950927	177.218610	1.632870e-10	-0.034774	6.751838e-07	-0.000029	-0.092887	-0.000076
1	-40.151249	-71.289786	-390.644700	156.940406	177.210378	4.042442e-07	-0.964540	2.172564e-06	-0.001422	-2.576627	-0.003798
2	-40.146303	-71.302198	-390.713778	156.865626	177.229361	1.701509e-07	-0.465100	3.932872e-06	-0.000922	-1.242375	-0.002464
3	-40.168626	-71.303232	-390.758887	157.019028	177.264076	2.036284e-10	0.060652	2.767689e-07	0.000032	0.162024	0.000085
4	-40.141835	-71.306699	-390.647256	156.895460	177.214655	3.324171e-08	0.315724	1.667388e-06	0.000408	0.843350	0.001089
...	...	...	...	...	...	...	...	...	...	...	...
10344	-40.158608	-71.286452	-390.621424	156.925743	177.219374	9.720124e-08	-0.751875	8.597060e-07	-0.000697	-2.008449	-0.001862
10345	-40.126567	-71.312560	-390.680826	156.850285	177.200106	3.305969e-08	0.431338	8.884518e-07	0.000407	1.152187	0.001086
10346	-40.160626	-71.311297	-390.702279	156.993680	177.252665	1.083228e-07	0.455123	2.614759e-06	0.000736	1.215745	0.001966
10347	-40.155516	-71.280032	-390.592207	156.913290	177.204329	8.472110e-07	-1.207476	2.905384e-06	-0.002058	-3.225542	-0.005498
10348	-40.138388	-71.313955	-390.658103	156.919275	177.215955	4.470688e-08	-0.457253	1.069128e-06	-0.000473	-1.221399	-0.001263

	dfb_Intercept	dfb_weight	dfb_age	dfb_sex	dfb_hdresult	cooks_d	standard_resid	hat_diag	dffits_internal	student_resid	dffits
0	-17.158012	-108.106234	-400.059818	202.240674	170.690229	1.250661e-09	-0.096237	6.751838e-07	-0.000079	-0.269924	-0.000222
1	-17.171344	-108.073769	-400.069005	202.227247	170.681097	4.279250e-07	-0.992389	2.172564e-06	-0.001463	-2.783609	-0.004103
2	-17.167957	-108.084024	-400.146277	202.143962	170.702485	1.448400e-07	-0.429115	3.932872e-06	-0.000851	-1.203578	-0.002387
3	-17.188084	-108.087620	-400.181324	202.302851	170.734082	7.164111e-11	0.035976	2.767689e-07	0.000019	0.100910	0.000053
4	-17.163713	-108.087206	-400.066351	202.171187	170.685385	3.974351e-08	0.345223	1.667388e-06	0.000446	0.968259	0.001250
...	...	...	...	...	...	...	...	...	...	...	...
10344	-17.179360	-108.069159	-400.044186	202.208774	170.690117	1.085013e-07	-0.794378	8.597060e-07	-0.000737	-2.228101	-0.002066
10345	-17.145698	-108.095634	-400.108588	202.126644	170.669345	2.747032e-08	0.393188	8.884518e-07	0.000371	1.102806	0.001039
10346	-17.180196	-108.093518	-400.121158	202.270055	170.720806	1.031553e-07	0.444134	2.614759e-06	0.000718	1.245716	0.002014
10347	-17.176483	-108.062504	-400.013326	202.198983	170.674809	9.174439e-07	-1.256529	2.905384e-06	-0.002142	-3.524455	-0.006008
10348	-17.158385	-108.098573	-400.085289	202.210135	170.687477	5.758677e-08	-0.518957	1.069128e-06	-0.000537	-1.455541	-0.001505

	df	sum_sq	mean_sq	F	PR(>F)
hlthstat	5.0	1543.076729	308.615346	31.693774	3.741562e-32
Residual	10343.0	100714.055131	9.737412	NaN	NaN

****intro****¶

Objectives¶

questions¶

1- Descriptive questions¶

2- Exploratory questions¶

3-predictive question¶

Analysis¶

descrptive analysis¶

exploratory analysis¶

bmi model¶

transformation¶

Weight least squaren bmi model¶

transformation¶

logestic highbp model¶

bpsystol_model¶

weight¶

hct_model¶

transformation¶

weight¶

wtransformation¶

diabetes_logistic_model¶

ANOVA¶

intro¶